Abstract
This thesis focuses on the time evolution of two-level and three level state quantum systems, both in mathematical and physical realization. This is one of the most fundamental problems for the time-dependent evolution of the quan-tum system. This thesis covers some coherent quantum control techniques, in-cluding some solvable models (Rabi oscillation, Landau-Zener transition, Rosen-Zener model, Allen-Eberly scheme), two-level adiabatic following and Stimu-lated Raman Adiabatic Passage (STIRAP) in the three-state quantum system and the shortcut to adiabaticity (STA). These methods are well-known mech-anisms for coherent quantum control, by employing for the two-level, three-level, even for the N-level quantum system. These mechanisms have a large number of applications to different quantum or classical systems, such as quan-tum computation (qubit state control), waveguide coupling system, light-matter interaction and even for wireless energy transfer and many others. One important objective for coherent quantum control addresses the transi-tion quantum state from initial state to target state, which is attentions at rapid, precise and robustness against the external varying parameters. These ?gure of merits of coherent quantum control are signi?cant. Firstly, we require rapid operators to our quantum system to be as fast as possible, to prevent the deco-herence of the quantum system. Secondly, precision is very important feature for the coherent quantum control, because the ?delity of results will determine its reliability. When the precision of the ?nal state is lower than the threshold, calculations of quantum computation are futile from the results. Finally, the ro-bustness against the external ?uctuation is also signi?cant for realistic physical implementation. By reason of the robustness, accurately manipulation external control parameters, including, the timing, amplitude, frequency, pulse shape of the laser pulse and geometry parameters, are arduous to control. Therefore, when we have some acceptable errors in these external parameters, the ?delity of results could be still lower than the threshold. To achieve these goals, a straightforward approach is to solve the Schrödinger equation by employing the most general two level Hamiltonian (solving the second order differential equation of Schrödinger equation), in some solvable model, such as Rabi oscillation, Landau-Zener transition, Rosen-Zener model and Allen-Eberly scheme. Since these methods have been proposed, increas-ing number of papers of quantum control had been researched to ?nd more the solvable models. However, it is not easy to ?nd other solvable models with advantages over well-known solvable models. Alternatively, by apply-ing the adiabatic following approximation, a new approach has been intro-duced into the area of quantum coherent control, both in two-level quantum adiabatic following and Stimulated Raman Adiabatic Passage in the three-state system. With adiabatic following approximation, we conveniently solve the Schrödinger equation with most general two level or three level Hamiltonian, by turning into the normal state to adiabatic state. Therefore we overcome the dif?cult of solving Schrödinger equation with most general Hamiltonian. An-other advantage of this technique has robustness against varying the external control parameters. However, according to the adiabatic following approxima-tion, the Hamiltonian with adiabatic basis require a longer time to process. To solve this problem, the shortcut of adiabaticity technique has already proposed in 2014, which enumerates an additional Hamiltonian to overcome the long processing time of adiabatic following. To summary, advantages of coherent quantum control are quantum transi-tion from initial state to target state with rapid, precise and robustness against the external varying parameters. Employing applications of coherent quantum control to quantum and classical systems is another larger aspect of researches and studies. Firstly, applications of coherent quantum control to achieve trans-ferring population (or intensity) for quantum and classical devices with rapid, precise and robustness. Furthermore, these applications bene?t to authenticate behaviors of the quantum coherent control and also fabrications of these de-vices have better understanding features the coherent quantum control to im-prove the performances. In this thesis, I conclude these quantum coherent con-trol methods and suggest novel applications to various quantum and classical systems, including atomic quantum system, waveguides coupler and design of coupling graphene device (electron waveguide coupler and Surface Plas-mon Polaritons). Because evolution population (intensity) of these systems is demonstrated by solving the time-dependent Schrödinger equation (for atomic quantum system) or coupled mode theory, which is equivalent to Schrödinger equation (for systems like coupled waveguide, electron waveguide coupler and Surface Plasmon Polaritons on graphene sheets). To summary of my work in this thesis, we present adiabatic following in a three-state quantum system subject to a single driving detuned driving ?eld and we show that depending on the initial state, several ?nal states can be prepared in a robust fashion. In addition, we employ the coherent quantum control to waveguide coupler. At the ?rst part of waveguide couplers’ design, we present a two-waveguide coupler which realizes complete achromatic all-optical switching. We derive an analytic solution for the electric ?eld propaga-tion, with hyperbolic-secant coupling strength and phase mismatch detuning. This study shows that the light switching is robust against small to moderate variations in the coupling strength and phase mismatch. We further consider the extended case of three coupled waveguides in an array to construct bidirec-tional achromatic light beam splitting. At second part of waveguide couplers’ design, we apply the shortcut of adiabaticity to extend our complete achromatic all-optical switching to achieve shorter device length and more robust against variations in the coupling strength and the phase mismatch. Furthermore, we propose a novel coupling between two graphene electron waveguides, in anal-ogy the optical waveguides. The design is based on the coherent quantum mechanical tunneling of Rabi oscillation between the two graphene electron waveguides. Based on this coupling mechanism, we propose that it can be used as an ultrafast electronic switching device. At the end, by using the Stim-ulated Raman Adiabatic Passage (STIRAP) Quantum Control Technique, we propose a novel directional coupler based on SPPs evolution in three layers of graphene sheets in some curved con?guration. Our calculated results show that the SPPs can be transferred ef?ciently from the input graphene sheet to the out-put graphene sheet, and the coupling is also robust that it is not sensitive to the length of the device con?guration’s parameters and excited SPPs wavelength.